Advertisement

Non-Self-Averaging of a Two-Person Game with Only Positive Spillover: A New Formulation of Avatamsaka’s Dilemma

Chapter

Abstract

In this game (Aruka 2001), selfishness may not be determined even if an agent selfishly adopts the strategy of defection. Individual selfishness can only be realized if the other agent cooperates, therefore gain from defection can never be assured by defection alone. The sanction by defection as a reaction of the rival agent cannot necessarily reduce the selfishness of the rival. In this game, explicit direct reciprocity cannot be guaranteed. Now we introduce different spillovers or payoff matrices, so that each agent may then be faced with a different payoff matrix. A ball in the urn is interpreted as the number of cooperators, and the urn as a payoff matrix. We apply Ewens’ sampling formula to our urn process in this game theoretic environment.

Keywords

Repeated Game Payoff Matrix White Ball Positive Spillover Payoff Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Akiyama E, Aruka Y (2006) Evolution of reciprocal cooperation in the Avatamsaka game. In: Namatame A, Kaizoji T, Aruka Y (eds) The complex networks of economic interaction. Springer, Heidelberg, pp 307–321CrossRefGoogle Scholar
  2. Aoki M (1996) New approaches to macroeconomic modeling: evolutionary stochastic dynamics, multiple equilibria, and externalities as field effects. Cambridge University Press, New YorkCrossRefGoogle Scholar
  3. Aoki M (2002) Modeling aggregate behavior and fluctuations in economics: stochastic views of interacting agents. Cambridge University Press, New YorkGoogle Scholar
  4. Aoki M (2008) Dispersion of growth paths of macroeconomic models in thermodynamic limits: two parameter Poisson-Dirichlet models. J Econ Interact Coord 3(1):3–14CrossRefGoogle Scholar
  5. Aoki M, Yoshikawa H (2006) Reconstructing macroeconomics: a perspective from statistical physics and combinatorial stochastic processes. Cambridge University Press, Cambridge, NYCrossRefGoogle Scholar
  6. Aoki M, Yoshikawa H (2007) Non-self-averaging in macroeconomic models: a criticism of modern micro-founded macroeconomics. Economics Discussion Papers (http://www.economics-ejournal.org) 2007-49 November 26
  7. Arthur BW (1994) Increasing returns and path dependence in the economy. University of Michigan Press, Ann ArborGoogle Scholar
  8. Arthur BW, Ermoliev YM, Kaniovski YM (1987) Path-dependent processes and the emergence of macro-structure. Eur J Oper Res 30:294–303CrossRefGoogle Scholar
  9. Aruka Y (2001) Avatamsaka game structure and experiment on the Web. In: Aruka Y (ed) Evolutionary controversies in economics. Springer, Tokyo, pp 115–132CrossRefGoogle Scholar
  10. Aruka Y (2001) Avatamsaka game experiment as a nonlinear Polya Urn Process. In: Terano T, Namatame A et al (eds) New frontiers on artificial intelligence. Springer, Berlin, pp 153–161Google Scholar
  11. Aruka Y (2004) How to measure social interactions via group selection? a comment: cultural group selection, coevolutionary processes, large-scale cooperation. J Econ Behav Org 53(1):41–47CrossRefGoogle Scholar
  12. Aruka Y (2007) The moral science of heterogeneous economic interaction in the face of complexity. In: Theodor Leiber (Hg) Dynamisches Denken und Handeln Philosophie und Wissenschaft in einer komplexen Welt, Festschrift fuer Klaus Mainzer zum 60. Geburtstag S.Hirzel Verlag Stuttgart, pp 171–183Google Scholar
  13. Aruka Y (2009) Book Review: Klaus Mainzer, Der kreative Zufall: wie das Neue in die Welt kommt (The creative chance. how novelty comes into the world (in German)). C.H. Beck, München, 2007, 283p. Evol Inst Econ Rev 5(2):307–316Google Scholar
  14. Bowles S (2004) Microeconomics: behavior, institutions, and evolution. Princeton University Press, PrincetonGoogle Scholar
  15. Canfield J, Hansen MV (2001) Chicken soup for the soul: 101 stories to open the heart and Rekindle the spirit (Chicken Soup for the Soul). Health Communications, Arlington, VAGoogle Scholar
  16. Ewens WJ (1972) The sampling theory of selectively neutral alleles. Theor Popul Biol 3:87–112CrossRefGoogle Scholar
  17. Flajolet P, Gabarro J, Pekari H (2005) Analytic urns annals of probability. Ann Probab 33(3):1200–1233CrossRefGoogle Scholar
  18. Fujiwara Y (2008) Book Review: Masanao Aoki and Hiroshi Yoshikawa, Reconstructing macroeconomics – a perspective from statistical physics and combinatorial stochastic processes. Cambridge University Press, 2007, 352 p. Evol Inst Econ Rev 4(2):313–317Google Scholar
  19. Henrich J (2004) Cultural group selection, coevolutionary processes and large-scale cooperation. J Econ Behav Org 53:3–36CrossRefGoogle Scholar
  20. Hildenbrand W (1994) Market demand. Princeton University Press, PrincetonGoogle Scholar
  21. Mainzer K (2007a) Thinking in complexity. The computational dynamics of matter, mind, and mankind, 5th edn. Springer, New YorkGoogle Scholar
  22. Mainzer K (2007b) Der kreative Zufall: wie das Neue in die Welt kommt (The Creative Chance. How Novelty Comes into the World). C. H. Beck, MünchenGoogle Scholar
  23. Mandelbrot BB, Hudson RL (2004) The (Mis)behavior of markets: a fractal view of risk, ruin and reward. Basic Books, New YorkGoogle Scholar
  24. Mitropoulos A (2004) Learning under minimal information: an experiment on mutual fate control. J Econ Psychol 22:523–557CrossRefGoogle Scholar
  25. Nowak MA, Sigmund K (1993) A strategy of win-stay lose-shift that outperforms tit-for-tat in the Prisoner’s Dilemma game. Nature 364:56–58CrossRefGoogle Scholar
  26. Pitman J (1995) Exchangeable and partially exchangeable random partitions. Probab Theory Relat Fields 12:145–158CrossRefGoogle Scholar
  27. Pitman J (2002) Lecture Notes of the Summer School on Probability, St. Flour, France (forthcoming from Springer)Google Scholar
  28. Price GR (1970) Selection and covariance. Nature 227:520–521CrossRefGoogle Scholar
  29. Price GR (1972) Extension of covariance selection mathematics. Ann Hum Genet 35:485–490CrossRefGoogle Scholar
  30. Tanimoto J (2007a) Promotion of cooperation by payoff noise in a 2 times 2 game. Phys Rev E 76:0411301–0411308Google Scholar
  31. Tanimoto J (2007b) Does a tag system effectively support emerging cooperation. J Theor Biol 247:756–764CrossRefGoogle Scholar
  32. Tanimoto J, Sagara H (2007) Relationship between dilemma occurrence and the existence of a weakly dominant strategy in a two-player symmetric game. Bio Syst 90:105–114Google Scholar
  33. Thibaut JW, Kelley HH (1959) The social psychology of groups. Wiley, New YorkGoogle Scholar
  34. Weidlich W (2002) Sociodynamics: a systematic approach to mathematical modeling in the social sciences. Taylor and Francis, LondonGoogle Scholar
  35. Weidlich W (2006) Intentions and principles of sociodynamics. Evol Inst Econ Rev 2(2):161–166Google Scholar
  36. Weidlich W (2007) Laudatio inofficialis für Prof. Dr. Dr. H. C. Mult, Hermann Haken anlasslich seines 80. Geburtstages (mimeo)Google Scholar
  37. Yamato H, Sibuya M (2000) Moments of some statistics of Pitman sampling formula. Bull Inform Cybernet 6:463–488Google Scholar
  38. Yamato H, Sibuya M (2003) Some topics on Pitman’s probabilistic partition. Stat Math 51:351–372Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Faculty of CommerceChuo UniversityTokyoJapan
  2. 2.Graduate School of Systems and Information EngineeringUniversity of TsukubaTsukubaJapan

Personalised recommendations